Determination of the Choice of Theoretical Method
for a Pyridine / Protonated Pyridine System
R. Gotwals
North Carolina School of Science and Mathematics, Durham, NC
Received 3 April, 2007; Accepted 26 April, 2007
Published online on Comp Chem Moodle (moodle.ncssm.edu)
Abstract: The choice of a theoretical method in computational chemistry is a critical
consideration for the computational chemistry practitioner. The choice of a theoretical
method is evaluated as applied to the protonation of the pyridine molecule, a benzene-like
cyclic organic compound containing a single nitrogen atom in the ring. Geometry
optimizations are performed on both a neutral pyridine molecule and a positively charged
pyridinium cation, where a proton is attached to the nitrogen atom. The optimizations are
performed using two semi-empirical methods, AM1 and PM3, using the MOPAC
software. Geometry optimizations are also performed using a density functional theory
(DFT) hybrid functional (B3LYP/6-31G(p,d) on both of the organics. Single point
energy calculations are performed on the proton using AM1 and PM3. A comparison of
the heats of formation for the reaction, calculated using Hess’ Law, shows that the DFT
theoretical method is significantly better (1.6% error as compared to the experimental
value) than that of the PM3 method (5% error) or the AM1 method (10% error).
Key words: theoretical method, model chemistry, pyridine, pyridinium, protonation, heats of formation
is conventional wisdom that ab initio quantum
chemical techniques are generally limited to
molecules that are under 100 atoms in size. The
practical number for ab initio calculations tends
to be closer to 50 atoms or less.
Introduction
One of the most critical decisions to be made by
the practitioner of computational chemistry is
that of choosing the most appropriate theoretical
method. The chemist must make a decision as to
which theoretical method is best suited for both
the problem to be solved, the accuracy of the
data needed to address the research question, and
the computational resources (software and
computational time) available to perform the
calculations.
The choice of a theoretical method is also
referred to as the model chemistry. In choosing a
model chemistry, one describes both the specific
form of the broad-level theoretical method. For
example, under the category of ab initio quantum
methods, one can choose a variety of methods,
such as Hartree-Fock, Moller Plessett, or one of
the Configuration Interaction (CI) methods.
These are typically referred to in describing the
model chemistry by the commonly accepted
acronyms, such as HF, MP2, or CIS,
respectively.
Most computational chemists have the
knowledge and resources to choose from one of
four methods: 1) molecular
mechanics/molecular dynamics; 2) semiempirical methods; 3) ab initio methods; and 4)
density functional theory (DFT) methods. These
four areas represent, in the broadest terms, the
four levels of theory, or theoretical methods that
can be applied to any computational chemistry
research problem. The choice of a theoretical
method is often predicated on logistical
considerations such as the amount of time one
has to perform the calculations, the amount of
computing resources available, the need to share
resources with other researchers, and the size of
the molecule. As an example of the last item, it
The model chemistry description, particularly for
the quantum methods (ab initio and DFT), also
includes a notation of the basis set used in the
calculation. The basis set represents that set of
numbers that is used to begin the determination
of the wavefunction, which in term determines
the atomic orbitals (AOs) and, using the linear
combination of atomic orbitals (LCAO)
approximation, the molecular orbitals (MOs).
As a general rule, the larger the basis set, the
1
more accurate the results of the calculation (and
also the more computing time needed to perform
those calculations!).
The protonated version of this molecule, known
as a pyridinium cation, adds a hydrogen to the
nitrogen atom, with a subsequent increase in the
charge of the molecule to a cation (positivelycharged ion):
In describing the model chemistry, a standard
format is used. The level of theory and the basis
set used to ensure that the molecule has been
optimized geometrically is first reported, and
then the level of theory used to perform the
calculations (separated by a double //) is
reported. For example, supposing that a
molecule has been optimized geometrically using
a Hartree-Fock level of theory with a STO-3G
basis set, then the calculations performed with a
Hartree-Fock level of the theory and a 631G(p,d) basis set, one would describe the
calculation as follows:
Following building, each molecule was
optimized using the “comprehensive cleanup”
molecular mechanics package found in the
WebMO molecular editor. Following this rough
optimization, pyridine and protonated pyridine
were optimized with MOPAC3, a semi-empirical
software package. Each of two molecules was
optimized three times from an initial build
followed by a comprehensive cleanup. The first
optimization was performed using MOPAC with
the AM1 basis set. The second was performed
with MOPAC using the PM3 basis set. Finally,
the third optimization was performed using
Gaussian 034 using a hybrid density functional
theory (DFT) model chemistry, specifically the
B3LYP/6-31G(p,d) model chemistry. In
addition, a proton (H+) was built. Using
MOPAC, single point energies (molecular
energies) were calculated using both the AM1
and PM3 basis sets.
HF/STO-3G//HF/6-31(p,d)
The choice of a theoretical method, or model
chemistry, is of considerable interest to the
computational practitioner. As more methods
are developed and more experience are gained in
the use of a variety of theoretical methods, so too
will our abilities to choose the right method for
the right problem. Our interest here is to
evaluate the optimal model chemistry for
studying the protonation of organic ring
structures. As a model organic structure, we
have chosen pyridine, a benzene-like ring
structure that has a substituted nitrogen atom,
replacing one of the carbons in the ring. Like
benzene, pyridine has an alternating double bond
structure reflecting the resonance of the
molecule. In this research, we are modeling the
protonation of the nitrogen, with the goal of
determining the change in the heat of formation
(∆Hf). The reaction heat of formation will be
calculated using Hess’ Law:
H f

rxn
 H f
products
 H f
Results and Discussion
For MOPAC calculations, all energies are
reported as heats of formation with units of
kilocalories per mole (kcal/mol). DFT
calculations resulted in energies reported in units
of hartrees (Eh). These energy values were
converted to kcal/mol energy units using the
conversion factor 1 Eh = 627.51 kcal/mol.
(1)
reac tants
Computational Approach
The data results are shown in Table 1.1.
Using the molecular editor builder of WebMO1
on the North Carolina High School
Computational Chemistry Server2, the molecules
pyridine, protonated pyridine, and a proton (H+)
were built. The structure of the pyridine
molecule is shown below:
Table 1.1 Computational Results
pyridine
N
2
References
The value for the proton for the DFT calculation
was obtained from literature5. The overall ∆Hf
for the reactions were calculated using Hess’
Law (Equation 1), based on the reaction:
1.
2.
Protonated pyridine --> Pyridine + H+
3.
Figure 1.1 shows a comparison of the ∆Hf for the
three theoretical methods.
4.
Figure 1.1. ∆Hf for methods
Percent error determinations for the three
methods were calculated using the experimental
value of –219.2 kcal/mol for the heat of
formation for the reaction. The percent error
calculations are reported in Table 1.1.
Conclusions
Based on the data and data analysis, the results
suggest that the more powerful quantum
chemical theoretical method – specifically, the
choice of the DFT hybrid functional – provides a
significant improvement in the accuracy of the
∆Hf for the protonation of pyridine. Both semiempirical methods using the AM1 and PM3
basis sets resulted in a percent error
determination greater than 10% (25.73% and
10.27%, respectively). It can be stated,
therefore, that the choice of the DFT hybrid
theoretical method is the most superior choice
for organic protonation methods. Further studies
on other organic moieties to substantiate this
finding are currently underway
5.
Acknowledgement
The author thanks Dr. Clyde Metz of the College
of Charleston, SC, and Dr. Shawn Sendlinger of
North Carolina Central University for assistance
with this work. Appreciation is also extended to
the Burroughs Wellcome Fund and the North
Carolina Science, Mathematics and Technology
Center for their funding support for the North
Carolina High School Computational Chemistry
Server.
3
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